# Assume that P (A) = P (B). Show that A = B.

We have to show that: A = B

Given: P (A) = P (B)

Let x be any element of set A,

P(A) is the power set of set A, hence it contains all the subsets of set A. Thus set A is contained in set P(A).

Now let C be an element of set B

Now, we have:

C B

A B

Similarly, we have:

B A

Now if A B and B ⊂ A

A = B

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RS Aggarwal - Mathematics